Card Range To Study

5 Cards in this Set

Point: a sizeless dot that holds a specific location or place of its own space.

Line: infinite set of collinear points that extends without limit in opposite directions.

Plane: an infiinite set of points that forms a boundless perfectly flat surface.

(SPACE)

Tools Used in Geometry

Definitions: Meaning of a word; a shape exists by definition.

Postulates: DUH statements that require no proof. We accept them as true.

Theorems: Statements that do require proof.

Corollary: The next natural assumption after a theorem.

Point Line Plane Postulates

P1: In space through a given point there exists a line for EVERY POSSIBLE pair of opposite directions in space.
P2: Through a given point in a plane, there exists one line for EVERY POSSIBLE pair of opposite directions within the plane. P3: It requires exactly 4 distinct points (non 3 of which are collinear) to establish a region of space.
P6: 2 distinct straight lines can intersect in exactly one point.
P8: An infinite # of planes may be passed through 1 straight line. P9: If a straight line does not intersect a plane at all, then the line is parallel to that plane.
P10: If a straight line intersects a plane in exactly one point, then the line does not lie in the plane.

Ruler Postulate

The points on a line can be matched, one-to-one, with the set of real numbers. The real # that corresponds with a point is the coordinate of the point. The distance, AB, between 2 points, A and B, on a line is equal to the absolute value of the difference between the coordinates of A and B.